Rowling began publicly hinting at the relationship from at least 2000.
Since the question seeks Rowling quotes, I thought I'd assemble an answer of public statements she made before she had finished writing the books. Hopefully the chronological progression of her decision-making is apparent. The quotes are almost entirely sourced from www.accio-quote.org.
As early as 1999 (before the publication of Goblet of Fire) she went as far as to seemingly rule out a Harry-Hermione relationship. She hinted at another relationship, which may have been a reference to Ron-Hermione:
JKR: Oh I like this one: "Do Harry and Hermione have a date?" No! They're, they're very platonic friends. But I won't answer for anyone else, nudge, nudge, wink, wink.
(National Press Club luncheon, 20th October 1999).
This is the clearest demonstration that she was happy to tease Ron-Hermione as a concept prior to the publication of Goblet of Fire. Obviously, the tension between Ron and Hermione features quite evidently in Goblet of Fire. After that book was published, in 2000, she confirmed that there was "something going on" between them in that book.
sammyohyeah: Is it just me, or was something going on between Ron and Hermione during the last half of GOF?
jkrowling_bn: yes, something's 'going on'...
jkrowling_bn: but Ron doesn't realise it yet...
jkrowling_bn: typical boy
(Barnes & Noble online chat, 20th October 2000).
Perhaps she was misdirecting and perhaps she hadn't definitively determined that Ron and Hermione would get together at that stage. Nevertheless, she was happy to strongly imply that a relationship between them was feasible. Such a comment is certainly consistent with her having decided to make Ron and Hermione an item in a future book. It's probable that she wouldn't have been so blatant both in her public remarks and in her writing if she wasn't sure the relationship would materialise in time.
In 2003, just before the publication of Order of the Phoenix, she again distanced herself from the notion that Hermione would enter into a relationship with Harry and said that Hermione and Ron had "more tension".
JKR And he, yes, [Harry] does have certain adolescent, um, rights of passage happen to him.
Couric: Any snogging with Hermione?
JKR: Hermione and Harry! Do you think so?
Couric: No I’m kidding.
JKR: Ron and Hermione, I would say, have more tension there.
(Dateline NBC Interview, 20th June 2003).
In Half-Blood Prince the chemistry between Ron and Hermione is pretty blatant. Ron dates Lavender Brown just to try and get in a relationship and Hermione responds with a huge amount of jealousy. Rowling seemed to see Half-Blood Prince as the confirmation that Ron and Hermione would be an item in the final book. In 2005, after the book was published, she again shot down the idea that Hermione would end up with Harry.
JKR: Well I think anyone who is still shipping Harry/Hermione after this book
ES: [whispered] Delusional!
JKR: Uh - no! But they need to go back and reread, I think.
(Mugglenet Interview, 16th July 2005).
In 2006, she regarded the question as obvious.
FAQ: Does Hermione love Ron or Harry?
JKR: I can't believe that some of you haven't worked this one out yet.
(www.jkrowling.com, 2nd March 2006).
She obviously didn't rule out Hermione loving one of Ron or Harry and, since she had gone to such pains to rule out Harry-Hermione, she was evidently teasing Ron-Hermione. Later that year she again implied that they would get together, and dismissed Hermione dating Harry.
"Then one bored afternoon, I googled 'Harry Potter'. Oh... my... God. I had NO idea. The shipping wars? For people who are over 18 who may not know about this - because I certainly didn't - it's like cyber gang warfare. People who wanted Harry and Hermione to end up together...[crowd screams]...they're still out there! Get over it! And other people who wanted Hermione and Ron...[crowd screams]...And there are very weird couplings as well, but we will not go anywhere near there."
(Event with Steven King and John Irving, 1st August 2006).
Pottermore also references a quote, probably from the same event, where Rowling discusses what Hermione would see in the Mirror of Erised. Apparently, she "would see her and her friends triumphant after their mission" but also see herself "closely entwined" with somebody else (possibly Ron).
"Hermione would also see herself closely entwined...with...another...person..."
("Clues J.K. Rowling gave us about the Harry Potter books: Harry’s friends and family", Pottermore, 2nd August 2006).
By this point Rowling was being very open about Hermione having feelings for another character. The context from Half-Blood Prince made it clear that person was Ron.
From the above quotes I'd deduce that Rowling was happy to publicly confirm the basis of a relationship between Ron and Hermione in 2000. She admits that there was "something going on" between them in Goblet of Fire. A year beforehand she teased that another relationship other than Harry-Hermione was in the offing but didn't clarify who she was referring to. After Half-Blood Prince she considered it more-or-less public knowledge that Ron and Hermione would become a couple.
None of this gives us a precise date when she decided that the relationship would happen. Presumably she planned the relationship before she began talking about it in interviews. The quote in Kyle Doyle's answer certainly indicates that she probably planned the relationship from the very beginning. Nevertheless, by the time Deathly Hallows was released readers had a pretty clear understanding that Ron and Hermione would likely become a couple at some point.